Early Medieval English medicine was well aware of the basic function of the circulatory system, although it did place the liver rather than the heart at the centre, given the liver's role in filtering and 'renewing' the blood, filtering out toxins and so forth:

It is extended on the right side as far as the colon, it has five lobes, it holds the kidneys, it is the home of the blood, and the making of the blood and the nurturer. When digestion and thinning of foods happen in the liver, then they change their colour and turn themselves into blood, and it gathers the clean blood and casts out the uncleanliness that is there

The 9th Century medical textbook known as Bald's Leechbook does, however, illustrate the heart (heortan) was known for its role of circulating blood around the body, even if the liver was, conceptually, its home:

and sends the blood mostly through four veins (ædra)* to the heart and thence beyond to the whole body as far as the outermost limbs.

/* Note here that ædra simply means 'vessels' and the translator Doyle has made the choice of semantically translating to 'vein' based on prevailing contemporary Galenist views on how blood functioned.

I say 'circulatory system' but it's most likely that an Early English Leac would have subscribed to the Galenist view that blood was "created" in the liver, pumped to the heart and from there distributed to the body and absorbed where needed, rather than circulated in a continuous process [Our current understanding dates from William Harvey's 1628 On the Motion of the Heart and Blood in Animals]. Nonetheless, it would have been understood that the beating of the heart was the pumping of blood through the ædra to the rest of the body.